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> I don't think a rectangular wave can propagate through the ether ... Of course it can. A square wave is just a series of discrete sine components, each of wh

by lutusp 13y ago

> I don't think a rectangular wave can propagate through the ether ... Of course it can. A square wave is just a series of discrete sine components, each of which will happily propagate through the air. If this were not true, WiFi wouldn't work -- it also relies on multiple, coordinated frequencies and complex modulation.

a-priori 13y ago
Right, in ideal hardware. The problem is that in order to transmit an ideal square wave, you need infinite bandwidth. The problem being that any real circuit has a finite band it operates on. It will filter the components of the wave that are outside of its bandwidth, leading to 'ringing' artifacts (Gibbs phenomenon).
- lutusp 13y ago
  > Right, in ideal hardware. The problem is that in order to transmit an ideal square wave, you need infinite bandwidth. On the contrary. An ideal square wave's higher harmonics decline rather quickly: http://en.wikipedia.org/wiki/Square_wave#Examining_the_square_wave http://en.wikipedia.org/wiki/Square_wave#Examining_the_squar... In other words, there's enough energy to cause problems at 2, 6, 10 ... times f, but at rapidly declining levels. > It will filter the components of the wave that are outside of its bandwidth, leading to 'ringing' artifacts ... Ringing artifacts are present in a system whose bandwidth rolls off abruptly. It's less significant in a system with a gradual drop-off in response, like a piece of wire acting as a broadband antenna.
baddox 13y ago
> A square wave is just a series of discrete sine components A true square wave would require an infinite series of discrete sine components, wouldn't it?
- lutusp 13y ago
  > A true square wave would require an infinite series of discrete sine components, wouldn't it? Yes, in principle, it represents an infinite series: http://en.wikipedia.org/wiki/Square_wave#Examining_the_square_wave http://en.wikipedia.org/wiki/Square_wave#Examining_the_squar... But as you can see, the higher harmonics decline quickly in energy.

by lutusp 13y ago

a-priori 13y ago

Right, in ideal hardware. The problem is that in order to transmit an ideal square wave, you need infinite bandwidth. The problem being that any real circuit has a finite band it operates on. It will filter the components of the wave that are outside of its bandwidth, leading to 'ringing' artifacts (Gibbs phenomenon).

lutusp 13y ago
> Right, in ideal hardware. The problem is that in order to transmit an ideal square wave, you need infinite bandwidth. On the contrary. An ideal square wave's higher harmonics decline rather quickly: http://en.wikipedia.org/wiki/Square_wave#Examining_the_square_wave http://en.wikipedia.org/wiki/Square_wave#Examining_the_squar... In other words, there's enough energy to cause problems at 2, 6, 10 ... times f, but at rapidly declining levels. > It will filter the components of the wave that are outside of its bandwidth, leading to 'ringing' artifacts ... Ringing artifacts are present in a system whose bandwidth rolls off abruptly. It's less significant in a system with a gradual drop-off in response, like a piece of wire acting as a broadband antenna.

baddox 13y ago

> A square wave is just a series of discrete sine components A true square wave would require an infinite series of discrete sine components, wouldn't it?

lutusp 13y ago
> A true square wave would require an infinite series of discrete sine components, wouldn't it? Yes, in principle, it represents an infinite series: http://en.wikipedia.org/wiki/Square_wave#Examining_the_square_wave http://en.wikipedia.org/wiki/Square_wave#Examining_the_squar... But as you can see, the higher harmonics decline quickly in energy.